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A Procedure for Estimating the Variance of the Population Mean in Rejective Sampling

Author

Listed:
  • Stefan Marius

    (Polytehnica University of Bucarest, Splaiul Independentei nr. 313, Bucarest, RO-060042, Romania.)

  • Hidiroglou Michael A.

    (Statistics Canada, Canada.)

Abstract

Rejective sampling was first introduced by Hájek in 1964 as a way to select a sample consisting uniquely of distinct units. If n denotes the fixed sample size, the n units are drawn independently with probabilities that may vary from unit to unit and the samples in which all units are not distinct are rejected. More generally, in rejective sampling, we select repeated samples according to a basic sampling design until a selected sample meets a specified balancing tolerance. Given a set of auxiliary variables, we consider a procedure in which the probability sample is rejected unless the sample mean of the auxiliary variables is within a specified distance of its corresponding population mean. The procedure represents an alternative to the well-known balanced cube method. In this article, we propose an estimator of the variance under the rejective sampling design. We also present the results of a Monte Carlo simulation study.

Suggested Citation

  • Stefan Marius & Hidiroglou Michael A., 2020. "A Procedure for Estimating the Variance of the Population Mean in Rejective Sampling," Journal of Official Statistics, Sciendo, vol. 36(1), pages 173-196, March.
    • Handle: RePEc:vrs:offsta:v:36:y:2020:i:1:p:173-196:n:9
    DOI: 10.2478/jos-2020-0009
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    References listed on IDEAS

    as
    1. Wayne A. Fuller & Jason C. Legg & Yang Li, 2017. "Bootstrap Variance Estimation for Rejective Sampling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1562-1570, October.
    2. Wayne A. Fuller, 2009. "Some design properties of a rejective sampling procedure," Biometrika, Biometrika Trust, vol. 96(4), pages 933-944.
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